Now that we know how to solve equations with whole numbers, we will look at two different methods for solving equations that have fractions in them. The first method uses what you know about operations with fractions to solve the equation and the second method involves using inverse operations to get rid of the fractions and then solving the equation with whole numbers. You'll see both methods below and you can choose which method you prefer.
Method 1: Using Operations with Fractions to Solve Equations
In this method, you will solve the equations the same way you did in the previous lesson, but instead of doing the operations with whole numbers, you will use the fractions given in the problem. Take a look at this example:
In this equation, we are solving for x. This means that we have to get rid of everything that's on the same side of the equation as the "x." Therefore, we have to get rid of the 1/3. We do this by using inverse operations. Since 1/3 is being added to "x", to cancel it out we have to subtract it on both sides of the equation:
When we do this operation, we get:
Solving equations using this method involves combining what you learned in the previous lesson about solving equations and what you learned in unit 1 about the different operations with fractions. If you don't like this method, there's another method you could use.
Method 2: Get rid of the fractions
Since the fraction bar means division, a fraction is basically dividing the numerator by the denominator. As we know, we can cancel out division by multiplying by the same number we are dividing by (for example, multiplying by 4 cancels out dividing by 4). Therefore, we can cancel out the division (and, therefore, get rid of the fractions) by multiplying each side of the equation by the denominators of each fraction. Take a look at this example:
This gets a little bit more complicated when the fractions in the problem do not already have the same denominator because then you have to multiply both sides of the equation by the denominator of each fraction (extra steps). Take a look at this example:
TASK: Which method do you prefer? Why do you prefer this method?
TASK: Open the document and complete the problems. Turn them in during class.
Method 1: Using Operations with Fractions to Solve Equations
In this method, you will solve the equations the same way you did in the previous lesson, but instead of doing the operations with whole numbers, you will use the fractions given in the problem. Take a look at this example:
In this equation, we are solving for x. This means that we have to get rid of everything that's on the same side of the equation as the "x." Therefore, we have to get rid of the 1/3. We do this by using inverse operations. Since 1/3 is being added to "x", to cancel it out we have to subtract it on both sides of the equation:
When we do this operation, we get:
Solving equations using this method involves combining what you learned in the previous lesson about solving equations and what you learned in unit 1 about the different operations with fractions. If you don't like this method, there's another method you could use.
Method 2: Get rid of the fractions
Since the fraction bar means division, a fraction is basically dividing the numerator by the denominator. As we know, we can cancel out division by multiplying by the same number we are dividing by (for example, multiplying by 4 cancels out dividing by 4). Therefore, we can cancel out the division (and, therefore, get rid of the fractions) by multiplying each side of the equation by the denominators of each fraction. Take a look at this example:
This gets a little bit more complicated when the fractions in the problem do not already have the same denominator because then you have to multiply both sides of the equation by the denominator of each fraction (extra steps). Take a look at this example:
TASK: Which method do you prefer? Why do you prefer this method?
TASK: Open the document and complete the problems. Turn them in during class.